Input Information for the Equipment Duty Planning.

The basic input for the equipment duty planning task consists of the trains that have been planned in the timetables. These tables specify the trains that should be available and other information such as the station of departure and arrival, the train number, the time of departure and arrival, the days of the week when the train actually drives, the period of the year when it drives, etc.

The characteristic of a train refers to the days in the week when the train actually drives. The characteristics are denoted by `R' or `N', where `R' means `drives' and N means `does not drive', followed by the numbers of the weekdays (where 1 stands for Monday, 2 for Tuesday, etc.). Thus when a train has `R' as characteristic, it drives every day of the week. The characteristic `N67' means that a train does not drive on Saturdays and Sundays. The letters `R' and `N' are interchangeable in the sense that they are each other's complement. Thus `N67' is equal to `R12345'. The characteristics are always written down in such a way that the smallest number of digits is used, i.e. there will be at most three digits after the letter `R' or `N'. Often, the characteristic is indicated by means of 7 bits (one bit per day of the week where `1' means `drives' and `0' means `does not drive'), e.g. `N67' = `1111100'.

Besides the number of days, trains in the timetables also receive a period that refers to the time of the year when they actually drive. Nine periods are distinguished: 01 (abbreviation: NCV) not during yearly holidays, 02 (NVS) not during school vacations, 03 (RTP) during the toeristic period, 04 (NWH) not in the winter, 05 (RWH) in the winter, 06 (NTP) not during toeristic period, 07 (RVS) during school vacation, 08 (RCV) during the yearly holidays, 09 () each day of the year. The periods are numbered in such a way that the sum of a period and its complement equals 09 (i.e. ``each day of the year''). Thus RTP (03) + NTP (06) = 09 ().

Table 1 shows some examples of trains that are specified in the timetables.

The planning experts at the Railway Company exploit graphical representations of the trains in the timetables. Such a representation is called a ``Place-time frame'' (X-t frame). The horizontal axis in this frame contains a time-scale of 24 hours while the vertical axis contains a set of stations. Trains are represented as lines in the X-t frame. Note, however, that an X-t frame does not necessarily display trains at one particular day since a train both receives a period and a characteristic (which may expand over more than one day). For example, in figure 1, the first train that departs from ASD (Amsterdam) has period 09 (whole year) and characteristic ``R''. This means that the train drives every day of the year.

In the passenger transport, trains are further organized in ``passenger relations''. A relation groups all the trains that drive between two specific stations. The relations are described by a numerical interval. The number associated with a particular train allows to determine to which passenger relation it belongs, i.e. trains receive numbers according to the relation to which they belong. There are several intervals of numbers that refer to special trains. Two of them are worth mentioning: 3000-3999 are P trains (trains only during rush hour) that depart before 1:59pm. 4000-4999 are P trains that depart after 2:00pm. Table 2 shows some examples.

Other types of information are required as input for the equipment duty planning:

1. Structure of lines and stations: Knowledge about the structure of lines and stations is important for various reasons. The operations performed by the equipment are constrained by the physical lines (e.g. electrified or not) and by the structure of the tracks in and around the stations (e.g. front changes for electrical engines in a terminal station require at least 5 minutes).

2. Equipment characteristics: The railway company disposes of different types of equipment (electrical and diesel engines, motor vehicles, shunting engines, etc.). Each of these types has different characteristics with respect to coupling possibilities, lines upon which they can drive, traction, etc.).

3. Data concerning maintenance: Each type of equipment has specific requirements with respect to maintenance and surveys. Two issues are of critical importance here: the location of the workshop(s) where the different types receive maintenance and the duration of specific maintenance programs.

4. Data concerning the durations of operations: As was already mentioned, the different operations that are performed by the material take up a certain amount of time. The human planner must have knowledge about the duration of the different operations in order to arrive at a full specification of the duties.

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